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Will an observer on the ground hear a sonic boom if a plane passes overhead at exactly the speed of sound? That is, the plane does not cross the sound barrier. The plane just hits Mach one - and continues to travel at that exact speed.

This is a bit of a problem because the speed of sound changes with altitude, so we assume it remains at the exact same altitude. I imagine there are other caveats also!

I would guess that there is a sonic boom, but I'm not sure.

mins
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vikram dhar
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    Another caveat people often miss: if the plane flies at Mach 0.999, but the airflow over the wing is faster than the incident flow... is the plane technically supersonic? – AEhere supports Monica Aug 11 '17 at 08:51
  • @AEhere But for the sound energy to concentrate in a shock wave, you need to consider the environment between the plane and the observer. Things that happen very close to the plane are not interesting. Actually, all jet planes would be technically supersonic by this consideration as their fan is supersonic :-) – yo' Aug 11 '17 at 10:02
  • Yes but the speed of sound for that specific environment: temperature, humidity, density, etc – jean Aug 11 '17 at 11:39
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    @AEhere When flow in some areas is supersonic and in other areas is subsonic it is called transsonic – TomMcW Aug 11 '17 at 18:15

3 Answers3

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Not only does it produce a sonic boom at Mach 1, it will be the loudest boom that that particular aircraft can produce. enter image description here Image source

In the picture, 4 is the shock wave. The one at M1 is vertical, and has all the concentrated pressure differential in it. An aircraft flying at supersonic speeds forms two shock cones, one at the nose and one at the tail, with a pressure distribution in between that spreads the pressure differential out.

Peter Kämpf
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Koyovis
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    But the total power contained in the shockwave must surely be higher at higher speed? Power is force times velocity, so I would imagine that the power dissipated by the shockwave grows quadratically with speed. – Sanchises Aug 11 '17 at 09:17
  • @Sanchises "power is force times velocity" -- why should it be so also for the vibrations the plane induces on the surrounding environment? (I don't say it isn't, I just don't see the reason.) – yo' Aug 11 '17 at 09:59
  • @Sanchises the output of the sonic boom itself is a step input in pressure at M=1, a more gradual pressure increase to the same end value when speed is higher. – Koyovis Aug 11 '17 at 10:15
  • @Sanchises the catch is in the figure .2 you see many shock waves "merging"/"adding" in a single big one boom – jean Aug 11 '17 at 13:04
  • @yo' The engines deliver a continuous amount of power (which is higher at higher velocity), which needs to be dissipated one way or another. While of course there are many ways to dissipate power, I would expect a large part of this power to be dissipated through the shockwave. – Sanchises Aug 11 '17 at 13:39
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    @Koyovis I do believe you, but I think the explanation is a bit lacking. I can see that the shock is spread out over a cone rather than a flat disk (so I suppose it scales with $\tan\alpha$ or something), but how does the intensity of the shockwave come in to play, if at all? – Sanchises Aug 11 '17 at 13:45
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No, if standard atmospheric conditions apply.

Since speed of sound is proportional to temperature and temperature normally decreases with altitude, the speed of the aircraft at Mach 1 is subsonic in warmer, lower air. This means also that the Mach shock will diffuse and be audible on the ground either as a protracted rumble or not at all, depending on the aircraft's altitude.

If you are close by, the boom is a sharp, very loud double-bang which can shatter windows. If the airplane is flying a few thousand feet overhead, you hear a muted rumble (still very distinct, though). If its altitude is above 10.000 ft and you are still on the ground, it will silently pass. Except in an inversion, of course.

Note that I assumed that the listener is located below the flight path of the aircraft. If that would not be the case, the noise of the aircraft diving below the listener altitude would be substantial.

Peter Kämpf
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  • Dear downvoters, if you don't understand physics but feel that an answer you don't comprehend is wrong, please educate yourself before rashly downvoting. – Peter Kämpf Jan 25 '24 at 14:44
  • Yes, this answer is more sensible than some of the others – Aadiraj Anil Jan 25 '24 at 16:09
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    I think the issue is that you and @Koyovis both have given correct answers, but they seemingly contradict one another. I might suggest you provide a sense of scale at which the altitude difference between the aircraft and the observer is significant enough to produce the atmospheric effect you describe. (perhaps in just a bit more detail than "depending on the altitude"...?) Because there is a pretty huge difference between a Mach 1.0 Concorde overhead at 35K' and an F-14 Tomcat 200' off the deck. – Michael Hall Jan 25 '24 at 16:16
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    In other words, maybe instead of opening with a hard "no" that those with a short attention span might not get past, try "yes, but..." – Michael Hall Jan 25 '24 at 16:22
  • @MichaelHall You're right, that short attention span. I have witnessed dozens of sonic booms but not even in a single case together with flight data. I've heard the sharp bangs and saw the airplane close by and heard the rumble and saw it flying higher up, but without data. – Peter Kämpf Jan 25 '24 at 19:56
  • @MichaelHall I think you're right about the seeming contradiction. I'm upvoting this one, but not Koyovis's one because this one provides factual principles which back up the claim (the very good observation that density increasing will mean the speed of the shock wave will be below the speed of sound). – Kenn Sebesta Jan 26 '24 at 13:50
  • @KennSebesta It's actually the increased temperature which will make the shock wave diffuse. BTW, I upvoted Koyovis's answer for the observation that the shock will be most intense at Mach 1. – Peter Kämpf Jan 26 '24 at 14:24
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Yes a plane at M1.0 would make a sonic boom. And yes it would be heard on the ground.

@Peter Kämpf and others who say no are demonstratively incorrect.

On Chuck Yeager’s first supersonic flight he took the X-1 to Mach 1.06…at 43,000 feet.

Mach 1 at that altitude is approximately 660 mph so 1.06 would be 700 mph.

He was flying over the Mojave desert, approx 5000 feet elevation. The speed of sound at 5000 is approximately 748 mph. Well above the 700 the X-1 was going.

His sonic boom was clearly heard by NASA observers on the ground.

constructionist
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    And you know the atmospheric conditions that day, don't you? And you know what was heard was a sharp bang, not a rumble? Impressive! – Peter Kämpf Jan 25 '24 at 14:58
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    @constructionist, do you have any references to support the data that you're providing? – ROIMaison Jan 26 '24 at 10:40
  • @ROIMaison Where should I begin? https://www.space.com/16709-breaking-the-sound-barrier.html https://www.washingtonpost.com/sf/brand-connect/lockheed-martin/quick-and-quiet/ https://www.wired.com/story/chuck-yeagers-1947-flight-inspired-supersonic-ambitions/ https://airandspace.si.edu/stories/editorial/breaking-sound-barrier-75th – constructionist Feb 14 '24 at 22:17
  • @PeterKämpf Play at around 4:30 for 10 seconds or so. https://www.youtube.com/watch?v=i_rFAo358bU – constructionist Feb 14 '24 at 22:23
  • @PeterKämpf Or here starting at about 2:20. "two sharp blasts roll across the desert" https://www.facebook.com/SmithsonianChannelAviationNation/videos/the-moment-chuck-yeager-broke-the-sound-barrier/573843757763244/ – constructionist Feb 14 '24 at 22:36